The automorphism group for $p$-central $p$-groups

Document Type: Research Paper

Author

University of Cambridge, UK

Abstract

A $p$-group $G$ is $p$-central if $G^{p}\le Z(G)$‎, ‎and $G$ is‎ ‎$p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,y\in‎ ‎G$‎. ‎We prove that for $G$ a finite $p^{2}$-abelian $p$-central‎ ‎$p$-group‎, ‎excluding certain cases‎, ‎the order of $G$ divides the‎ ‎order of $\text{Aut}(G)$‎.

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